### Home > INT3 > Chapter 10 > Lesson 10.3.1 > Problem10-145

10-145.

What is the sum of each of the infinite geometric series? If it is not possible to calculate the sum, explain why not. Homework Help ✎

1. $8 + 4 + 2 + \ldots$

Find the common ratio.

$\frac{4}{8}=\frac{1}{2}$

$\frac{2}{4}=\frac{1}{2}$

Use the equation for an infinite geometric series:

$\displaystyle\sum_{n=1}^{\infty}{ar^{n-1}}=\frac{a}{1-r}$

$16$

1. $3 + 9 + 27 + 81 + \ldots$

See part (a).

Not possible. $r>1$, and the terms keep increasing.